-
1
-
-
0029719917
-
Generating hard instances of lattice problems
-
ACM
-
M. Ajtai. Generating hard instances of lattice problems (extended abstract). In Proc. of STOC 1996, pages 99-108. ACM, 1996.
-
(1996)
Proc. of STOC 1996
, pp. 99-108
-
-
Ajtai, M.1
-
2
-
-
33746682361
-
Random lattices and a conjectured 0-1 law about their polynomial time computable properties
-
IEEE
-
M. Ajtai. Random lattices and a conjectured 0-1 law about their polynomial time computable properties. In Proc. of FOCS 2002, pages 13-39. IEEE, 2002.
-
(2002)
Proc. of FOCS 2002
, pp. 13-39
-
-
Ajtai, M.1
-
3
-
-
0038784608
-
The worst-case behavior of Schnorr's algorithm approximating the shortest nonzero vector in a lattice
-
ACM
-
M. Ajtai. The worst-case behavior of Schnorr's algorithm approximating the shortest nonzero vector in a lattice. In Proc. of STOC 2003, pages 396-406. ACM, 2003.
-
(2003)
Proc. of STOC 2003
, pp. 396-406
-
-
Ajtai, M.1
-
5
-
-
51249173801
-
On Lovász lattice reduction and the nearest lattice point problem
-
L. Babai. On Lovász lattice reduction and the nearest lattice point problem. Combinatorica, 6:1-13, 1986.
-
(1986)
Combinatorica
, vol.6
, pp. 1-13
-
-
Babai, L.1
-
7
-
-
24944534187
-
-
C. Batut, K. Belabas, D., Bernardi, H. Cohen, and M. Olivier. PARI/GP computer package version 2. Av. at http://pari.math.u-bordeaux.fr/.
-
PARI/GP Computer Package Version 2
-
-
Batut, C.1
Belabas, K.2
Bernardi, D.3
Cohen, H.4
Olivier, M.5
-
8
-
-
0003806299
-
-
Rational quadratic forms, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London
-
J. W. S. Cassels. Rational quadratic forms, volume 13 of London Mathematical Society Monographs. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1978.
-
(1978)
London Mathematical Society Monographs
, vol.13
-
-
Cassels, J.W.S.1
-
10
-
-
0001494997
-
Small solutions to polynomial equations, and low exponent RSA vulnerabilities
-
D. Coppersmith. Small solutions to polynomial equations, and low exponent RSA vulnerabilities. Journal of Cryptology, 10(4):233-260, 1997.
-
(1997)
Journal of Cryptology
, vol.10
, Issue.4
, pp. 233-260
-
-
Coppersmith, D.1
-
11
-
-
84958655849
-
Public-key cryptosystems from lattice reduction problems
-
Proc. of Crypto 1997, Springer-V
-
O. Goldreich, S. Goldwasser, and S. Halevi. Public-key cryptosystems from lattice reduction problems. In Proc. of Crypto 1997, volume 1294 of LNCS, pages 112-131. Springer-V., 1997.
-
(1997)
LNCS
, vol.1294
, pp. 112-131
-
-
Goldreich, O.1
Goldwasser, S.2
Halevi, S.3
-
12
-
-
0042671501
-
On the equidistribution of Hecke points
-
D. Goldstein and A. Mayer. On the equidistribution of Hecke points. Forum Mathematicum, 15:165-189, 2003.
-
(2003)
Forum Mathematicum
, vol.15
, pp. 165-189
-
-
Goldstein, D.1
Mayer, A.2
-
15
-
-
24944510964
-
Extraits de lettres de M. Hermite à M. Jacobi sur différents objets de la théorie des nombres, deuxième lettre
-
C. Hermite. Extraits de lettres de M. Hermite à M. Jacobi sur différents objets de la théorie des nombres, deuxième lettre. Journal für die reine und angewandte Mathematik, 40:279-290, 1850.
-
(1850)
Journal für Die Reine und Angewandte Mathematik
, vol.40
, pp. 279-290
-
-
Hermite, C.1
-
16
-
-
84947808606
-
NTRU: A ring based public key cryptosystem
-
Proc. of ANTS III, Springer-V
-
J. Hoffstein, J. Pipher, and J. H. Silverman. NTRU: a ring based public key cryptosystem. In Proc. of ANTS III, volume 1423 of LNCS, pages 267-288. Springer-V., 1998.
-
(1998)
LNCS
, vol.1423
, pp. 267-288
-
-
Hoffstein, J.1
Pipher, J.2
Silverman, J.H.3
-
17
-
-
84958979810
-
Segment LLL-reduction of lattice bases with floating-point orthogonalization
-
Proc. of CALC '01, Springer-V
-
H., Koy and C. P. Schnorr. Segment LLL-reduction of lattice bases with floating-point orthogonalization. In Proc. of CALC '01, volume 2146 of LNCS, pages 81-96. Springer-V., 2001.
-
(2001)
LNCS
, vol.2146
, pp. 81-96
-
-
Koy, H.1
Schnorr, C.P.2
-
18
-
-
34250244723
-
Factoring polynomials with rational coefficients
-
A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovász. Factoring polynomials with rational coefficients. Mathematische Annalen, 261:513-534, 1982.
-
(1982)
Mathematische Annalen
, vol.261
, pp. 513-534
-
-
Lenstra, A.K.1
Lenstra Jr., H.W.2
Lovász, L.3
-
19
-
-
0344838262
-
Integer programming with a fixed number of variables
-
Mathematisch Instituut, Universiteit van Amsterdam
-
H. W. Lenstra, Jr. Integer programming with a fixed number of variables. Technical report 81-03, Mathematisch Instituut, Universiteit van Amsterdam, 1981.
-
(1981)
Technical Report
, vol.81
, Issue.3
-
-
Lenstra Jr., H.W.1
-
20
-
-
0020845921
-
Integer programming with a fixed number of variables
-
H. W. Lenstra, Jr. Integer programming with a fixed number of variables. Mathematics of Operations Research, 8(4):538-548, 1983.
-
(1983)
Mathematics of Operations Research
, vol.8
, Issue.4
, pp. 538-548
-
-
Lenstra Jr., H.W.1
-
23
-
-
24944584767
-
Floating-point LLL revisited
-
Proc. of Eurocrypt 2005, Springer-V
-
P. Q. Nguyen and D. Stehlé. Floating-point LLL revisited. In Proc. of Eurocrypt 2005, volume 3494 of LNCS, pages 215-233. Springer-V., 2005.
-
(2005)
LNCS
, vol.3494
, pp. 215-233
-
-
Nguyen, P.Q.1
Stehlé, D.2
-
24
-
-
33846867921
-
The two faces of lattices in cryptology
-
Proc. of CALC '01, 2146 Springer-V
-
P. Q. Nguyen and J. Stern. The two faces of lattices in cryptology. In Proc. of CALC '01, volume 2146 of LNCS, pages 146-180. Springer-V., 2001.
-
(2001)
LNCS
, pp. 146-180
-
-
Nguyen, P.Q.1
Stern, J.2
-
25
-
-
0002114928
-
The rise and fall of knapsack cryptosystems
-
Proc. of Cryptology and Computational Number Theory, AMS
-
A. M. Odlyzko. The rise and fall of knapsack cryptosystems. In Proc. of Cryptology and Computational Number Theory, volume 42 of Proc. of Symposia in Applied Mathematics, pages 75-88. AMS, 1989.
-
(1989)
Proc. of Symposia in Applied Mathematics
, vol.42
, pp. 75-88
-
-
Odlyzko, A.M.1
-
27
-
-
0023532388
-
A hierarchy of polynomial lattice basis reduction algorithms
-
C. P. Schnorr. A hierarchy of polynomial lattice basis reduction algorithms. Theoretical Computer Science, 53:201-224, 1987.
-
(1987)
Theoretical Computer Science
, vol.53
, pp. 201-224
-
-
Schnorr, C.P.1
-
28
-
-
38249029857
-
A more efficient algorithm for lattice basis reduction
-
C. P. Schnorr. A more efficient algorithm for lattice basis reduction. Journal of Algorithms, 9(1):47-62, 1988.
-
(1988)
Journal of Algorithms
, vol.9
, Issue.1
, pp. 47-62
-
-
Schnorr, C.P.1
-
29
-
-
33846200465
-
Lattice basis reduction: Improved practical algorithms and solving subset sum problems
-
C. P. Schnorr and M. Euchner. Lattice basis reduction: improved practical algorithms and solving subset sum problems. Mathematics of Programming, 66:181-199, 1994.
-
(1994)
Mathematics of Programming
, vol.66
, pp. 181-199
-
-
Schnorr, C.P.1
Euchner, M.2
-
30
-
-
84941157879
-
-
NTL, Number Theory Library
-
V. Shoup. NTL, Number Theory Library. Av. at http://www.shoup.net/ntl/.
-
-
-
Shoup, V.1
-
31
-
-
0001680397
-
A mean value theorem in geometry of numbers
-
C. L. Siegel. A mean value theorem in geometry of numbers. Annals of Mathematics, 46(2):340-347, 1945.
-
(1945)
Annals of Mathematics
, vol.46
, Issue.2
, pp. 340-347
-
-
Siegel, C.L.1
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